A variationally consistent generalized variable formulation of the elastoplastic rate problem

Claudia Comi; Umberto Perego

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1991)

  • Volume: 2, Issue: 2, page 177-190
  • ISSN: 1120-6330

Abstract

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The elastoplastic rate problem is formulated as an unconstrained saddle point problem which, in turn, is obtained by the Lagrange multiplier method from a kinematic minimum principle. The finite element discretization and the enforcement of the min-max conditions for the Lagrangean function lead to a set of algebraic governing relations (equilibrium, compatibility and constitutive law). It is shown how important properties of the continuum problem (like, e.g., symmetry, convexity, normality) carry over to the discrete problem if «generalized variables» are used in the discretization. A couple of dual kinematic and static minimum properties in generalized variables are finally derived.

How to cite

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Comi, Claudia, and Perego, Umberto. "A variationally consistent generalized variable formulation of the elastoplastic rate problem." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 2.2 (1991): 177-190. <http://eudml.org/doc/244248>.

@article{Comi1991,
abstract = {The elastoplastic rate problem is formulated as an unconstrained saddle point problem which, in turn, is obtained by the Lagrange multiplier method from a kinematic minimum principle. The finite element discretization and the enforcement of the min-max conditions for the Lagrangean function lead to a set of algebraic governing relations (equilibrium, compatibility and constitutive law). It is shown how important properties of the continuum problem (like, e.g., symmetry, convexity, normality) carry over to the discrete problem if «generalized variables» are used in the discretization. A couple of dual kinematic and static minimum properties in generalized variables are finally derived.},
author = {Comi, Claudia, Perego, Umberto},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Plasticity; Finite elements; Generalized variables; Extremum properties; generalized variables; extremum properties; convexity of generalized yield functions; unconstrained saddle point problem; Lagrange multiplier method; kinematic minimum principle; min-max conditions; set of algebraic governing relations},
language = {eng},
month = {6},
number = {2},
pages = {177-190},
publisher = {Accademia Nazionale dei Lincei},
title = {A variationally consistent generalized variable formulation of the elastoplastic rate problem},
url = {http://eudml.org/doc/244248},
volume = {2},
year = {1991},
}

TY - JOUR
AU - Comi, Claudia
AU - Perego, Umberto
TI - A variationally consistent generalized variable formulation of the elastoplastic rate problem
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1991/6//
PB - Accademia Nazionale dei Lincei
VL - 2
IS - 2
SP - 177
EP - 190
AB - The elastoplastic rate problem is formulated as an unconstrained saddle point problem which, in turn, is obtained by the Lagrange multiplier method from a kinematic minimum principle. The finite element discretization and the enforcement of the min-max conditions for the Lagrangean function lead to a set of algebraic governing relations (equilibrium, compatibility and constitutive law). It is shown how important properties of the continuum problem (like, e.g., symmetry, convexity, normality) carry over to the discrete problem if «generalized variables» are used in the discretization. A couple of dual kinematic and static minimum properties in generalized variables are finally derived.
LA - eng
KW - Plasticity; Finite elements; Generalized variables; Extremum properties; generalized variables; extremum properties; convexity of generalized yield functions; unconstrained saddle point problem; Lagrange multiplier method; kinematic minimum principle; min-max conditions; set of algebraic governing relations
UR - http://eudml.org/doc/244248
ER -

References

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  10. SIMO, J. C. - KENNEDY, J. G. - TAYLOR, R. L., Complementary mixed finite element formulations for elastoplasticity. Comp. Meth. Appl. Mech. Eng., vol. 74, 1989, 177-206. Zbl0687.73064MR1020622DOI10.1016/0045-7825(89)90102-3
  11. COMI, C. - MAIER, G. - PEREGO, U., Generalized variable finite element modelling and extremum theorems in stepwise holonomic elastoplasticity with internal variables. To appear. Zbl0761.73107MR1162380DOI10.1016/0045-7825(92)90133-5
  12. CAPURSO, M. - MAIER, G., Incremental elastoplastic analysis and quadratic optimization. Meccanica, vol. 2, 1970, 107-116. Zbl0198.58301
  13. HALPHEN, B. - NGUYEN, Q. S., Sur les matériaux standards généralisés. J. de Mécanique, vol. 14, 1975, 39-63. Zbl0308.73017MR416177
  14. LEMAITRE, J. - CHABOCHE, J. L., Mécanique des matériaux solides. Dunod, Paris1985. 
  15. COMI, C. - MAIER, G., Extremum theorem and convergence criterion for an iterative solution to the finite-step problem in elastoplasticity with mixed nonlinear hardening. Eur. J. Mech., A/Solids, vol. 9, 1990, 563-585. Zbl0807.73079MR1082827

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